Joined objects won't move with rig
You've probably parented the mesh to the skeleton before joining additional parts to it. Thus vertices of the new parts don't belong to any vertices groups, created by "Parent with automatic weights" operation. If it's only about the helmet, the easiest way to fix that would be to separate it again from the body mesh and parent it to the head bone. If you're planning to add some equipment also to the chest, usually the way to go about it would be to keep that separate and use Mesh Deform modifier to control the character, cause it's usually hard to get perfect weights on fragments that are not physically connected (not just joined, but with common edges) with the main mesh.